diatomicCvHigh
plain-language theorem explainer
Recognition Science sets the high-temperature constant-volume heat capacity for diatomic gases to 7/2 R. This value encodes seven active quadratic modes per molecule once temperature activates all 8-tick phases. Thermodynamic derivations in the RS framework cite the assignment when applying equipartition above the vibrational threshold. The definition is a direct numerical assignment to the gas constant with no further reduction.
Claim. The high-temperature molar heat capacity at constant volume for a diatomic ideal gas equals $7/2 R$, where $R$ is the gas constant.
background
The module states its goal as deriving heat capacity formulas from 8-tick mode counting. Heat capacity is introduced as $C_V = (∂U/∂T)_V$ under classical equipartition, where each quadratic mode receives $kT/2$. In RS each spatial direction carries eight possible phases, yet only modes satisfying $T > ℏω/k_B$ remain active and contribute. The upstream tick definition supplies the fundamental time quantum $τ_0 = 1$ used to discretize these phases.
proof idea
This is a direct definition that assigns the constant 7/2 times the gas constant. It encodes the high-temperature regime in which translational, rotational, and vibrational modes are all active within the 8-tick counting scheme.
why it matters
The definition supplies the high-temperature diatomic limit inside the THERMO-004 module. It rests on the eight-tick octave (T7) and mode activation rules from the foundation. No downstream results are listed, yet the assignment supports later thermodynamic ratios and connects to the Recognition Composition Law through consistent mode counting.
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